$A$ car is moving on a circular path of radius $500 \ m$ with a speed of $30 \ m/s$. If the speed is increasing at a rate of $2 \ m/s^2$,the net acceleration will be ......... $m/s^2$.

$A$ particle moves in a circular path of radius $R$ with an angular velocity $\omega = a - bt$,where $a$ and $b$ are positive constants and $t$ is time. The magnitude of the acceleration of the particle after time $t = \frac{2a}{b}$ is:

The velocity and acceleration vectors of a particle undergoing circular motion are $\overrightarrow{v} = 2 \hat{i} \text{ m/s}$ and $\overrightarrow{a} = 2 \hat{i} + 4 \hat{j} \text{ m/s}^2$ respectively at an instant of time. The radius of the circle is $........ \text{ m}$.

The acceleration of a train travelling with a speed of $400 \, m/s$ as it goes round a curve of radius $160 \, m$ is:

The angular velocity of a particle of a rigid body is not constant. Which of the following statements is true?

$A$ stone tied to the end of a string $80\; cm$ long is whirled in a horizontal circle with a constant speed. If the stone makes $14$ revolutions in $25\; s$,what is the magnitude and direction of acceleration of the stone?